The infrared spectra of the silicon tetrafluoride molecule (SiF4) recorded on the AILES Beamline of the SOLEIL Synchrotron facility, have been studied in the range where the combination bands ν1+ν3, ν1+ν4, ν2+ν3 and ν2+ν4 are located. For each band, between 1100 and more than 2300 lines have been assigned and fitted with the effective Hamiltonian model for J values up to 55 (up to 82 for ν1+ν3). The obtained set of spectroscopic parameters allows one to reproduce experimentally obtained line positions with a root mean square deviation better than drms = 0.863 × 10−3 cm−1 .